School State Graduation Rate (%) % of Classes Under 20 Student/Faculty Ratio Alu
ID: 3290695 • Letter: S
Question
School
State
Graduation Rate (%)
% of Classes Under 20
Student/Faculty Ratio
Alumni Giving Rate (%)
Boston College
MA
85
39
13
25
Brandeis University
MA
79
68
8
33
Brown University
RI
93
60
8
40
California Institute of Technology
CA
85
65
3
46
Carnegie Mellon University
PA
75
67
10
28
Case Western Reserve University
OH
72
52
8
31
College of William and Mary
VA
89
45
12
27
Columbia University
NY
90
69
7
31
Cornell University
NY
91
72
13
35
Dartmouth College
NH
94
61
10
53
Duke University
NC
92
68
8
45
Emory University
GA
84
65
7
37
Georgetown University
DC
91
54
10
29
Harvard University
MA
97
73
8
46
John Hopkins University
MD
89
64
9
27
Lehigh University
PA
81
55
11
40
Massachusetts Inst. of Technology
MA
92
65
6
44
New York University
NY
72
63
13
13
Northwestern University
IL
90
66
8
30
Pennsylvania State University
PA
80
32
19
21
Princeton University
NJ
95
68
5
67
Rice University
TX
92
62
8
40
Stanford University
CA
92
69
7
34
Tufts University
MA
87
67
9
29
Tulane University
LA
72
56
12
17
U. of California-Berleley
CA
83
58
17
18
U. of California-Davis
CA
74
32
19
7
U. of California-Irvine
CA
74
42
20
9
U. of California-Los Angeles
CA
78
41
18
13
U. of California-San Diego
CA
80
48
19
8
U. of California-Santa Barbara
CA
70
45
20
12
U. of Chicago
IL
84
65
4
36
U. of Florida
FL
67
31
23
19
U. of Illinois-Urbana Champaign
IL
77
29
15
23
U. of Michigan-Ann Arbor
MI
83
51
15
13
U. of North Carolina-Chapel Hill
NC
82
40
16
26
U. of Notre Dame
IN
94
53
13
49
U. of Pennsylvania
PA
90
65
7
41
U. of Rochester
NY
76
63
10
23
U. of Southern California
CA
70
53
13
22
U. of Texas-Austin
TX
66
39
21
13
U. of Virginia
VA
92
44
13
28
U. of Washington
WA
70
37
12
12
U. of Wisconsin-Madison
WI
73
37
13
13
Vanderbuilt University
TN
82
68
9
31
Wake Forest University
NC
82
59
11
38
Washington University - St. Louis
MO
86
73
7
33
Yale University
CT
94
77
7
50
Case 4 (Operations Management Application):
This case study involves Alumni, which are an important source of revenue
for colleges and universities. If administrators could determine the factors
that influence increases in the percentage of alumni who make a donation
(alumni giving rate), they might be able to implement policies that could
lead to increased revenue. Research shows that students who are more
satisfied with their contact with teachers are more likely to graduate. As a
result, one might suspect that smaller class sizes and lower student-
faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation.
The managerial report should contain such as:
1.Choose the best-fit simple linear regression analysis to develop an
estimated equation that could be used to predict the alumni-giving rate. (20%)
2.Use the multiple linear regression analysis to develop an estimated
regression equation that could be used to predict the alumni-giving rate given the graduation rate, the percentage of classes with fewer than 20 students, and the student-faculty ratio. Is it a better fit compared with your answer in (1)? Any multicollinearity exists? Please show the correlation coefficients to comment.(20%)
3.What conclusion and recommendation can you derive from F and t
tests in (2)? (20%)
4.With the multiple linear regression equation in (2), what will be the alumni-giving rate with the graduation rate as 85%, 60% of classes with fewer than 20 students, and student-faculty ratio as 12? (20%)
5.Any possible modification you suggest for a better-fit multiple linear
regression model? Adding or dropping independent variable(s)? Change to any nonlinear model? Explain your suggestion. (20%)
School
State
Graduation Rate (%)
% of Classes Under 20
Student/Faculty Ratio
Alumni Giving Rate (%)
Boston College
MA
85
39
13
25
Brandeis University
MA
79
68
8
33
Brown University
RI
93
60
8
40
California Institute of Technology
CA
85
65
3
46
Carnegie Mellon University
PA
75
67
10
28
Case Western Reserve University
OH
72
52
8
31
College of William and Mary
VA
89
45
12
27
Columbia University
NY
90
69
7
31
Cornell University
NY
91
72
13
35
Dartmouth College
NH
94
61
10
53
Duke University
NC
92
68
8
45
Emory University
GA
84
65
7
37
Georgetown University
DC
91
54
10
29
Harvard University
MA
97
73
8
46
John Hopkins University
MD
89
64
9
27
Lehigh University
PA
81
55
11
40
Massachusetts Inst. of Technology
MA
92
65
6
44
New York University
NY
72
63
13
13
Northwestern University
IL
90
66
8
30
Pennsylvania State University
PA
80
32
19
21
Princeton University
NJ
95
68
5
67
Rice University
TX
92
62
8
40
Stanford University
CA
92
69
7
34
Tufts University
MA
87
67
9
29
Tulane University
LA
72
56
12
17
U. of California-Berleley
CA
83
58
17
18
U. of California-Davis
CA
74
32
19
7
U. of California-Irvine
CA
74
42
20
9
U. of California-Los Angeles
CA
78
41
18
13
U. of California-San Diego
CA
80
48
19
8
U. of California-Santa Barbara
CA
70
45
20
12
U. of Chicago
IL
84
65
4
36
U. of Florida
FL
67
31
23
19
U. of Illinois-Urbana Champaign
IL
77
29
15
23
U. of Michigan-Ann Arbor
MI
83
51
15
13
U. of North Carolina-Chapel Hill
NC
82
40
16
26
U. of Notre Dame
IN
94
53
13
49
U. of Pennsylvania
PA
90
65
7
41
U. of Rochester
NY
76
63
10
23
U. of Southern California
CA
70
53
13
22
U. of Texas-Austin
TX
66
39
21
13
U. of Virginia
VA
92
44
13
28
U. of Washington
WA
70
37
12
12
U. of Wisconsin-Madison
WI
73
37
13
13
Vanderbuilt University
TN
82
68
9
31
Wake Forest University
NC
82
59
11
38
Washington University - St. Louis
MO
86
73
7
33
Yale University
CT
94
77
7
50
Explanation / Answer
1.
the best-fit simple linear regression analysis to develop an estimated equation that could be used to predict the alumni-giving rate is given in figure 1 which explain 57% data.
2.
3.
SUMMARY OUTPUT Regression Statistics Multiple R 0.836625 R Square 0.699941 Adjusted R Square 0.679482 Standard Error 7.609725 Observations 48 ANOVA df SS MS F Significance F Regression 3 5943.531 1981.177 34.21255 1.43E-11 Residual 44 2547.948 57.90791 Total 47 8491.479 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -20.7201 17.52137 -1.18256 0.243333 -56.0321 14.59186 Graduation Rate (%) 0.748183 0.16596 4.508213 4.8E-05 0.413712 1.082653 % of Classes Under 20 0.029041 0.139321 0.208444 0.835844 -0.25174 0.309824 Student/Faculty Ratio -1.19201 0.386723 -3.08234 0.003538 -1.9714 -0.41262Related Questions
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